There is no "legal" BSA way to present an award. As long as it is in a meaningful ceremony, it is pretty much whatever goes.
However - Before you start planning your son's own, individual, AOL ceremony, I recommend that you talk to his den leader, and see what kind of ceremony the Pack is planning for the Webelos den. I do not see a problem with adjusting the ceremony a bit to include his Uncle presenting his AOL award, instead of the DL/CM/OA member, etc, but you SHOULD talk to them first.
As for your brother being in uniform - is he currently a registered member of BSA? If YES, then wearing his current uniform with his Eagle Medal pinned over his Eagle square knot would be very appropriate. If he is NOT a current registered BSA member, then he should wear regular clothes (a suit if he feels like it would be nice). The BSA uniform can ONLY be worn by a registered member of BSA. It would be fine for him to wear his Eagle Award on his suit jacket. There is also the silver miniature Eagle tack pin, and the National Eagle Scout Association pin, which are both authorized for civilian wear.
